In this problem, Black cannot live unconditionally. We start off by playing at , which reduces the liberties of the
stones by one.
If wants to kill, then the number of liberties of the
stones is further reduced by one. This enables
to start a ko for life.
Although also reduces the number of liberties of the
stones by one,
destroys the eye and does not have to reduce the number of liberties of the
stones. So Black loses the capturing race.
Although cutting at seems like a reasonable move,
is a clever move that kills.